Small Noise Analysis of Non-Parametric Closed-Loop Identification
arxiv(2024)
摘要
We revisit the problem of non-parametric closed-loop identification in
frequency domain; we give a brief survey of the literature and provide a small
noise analysis of the direct, indirect, and joint input-output methods when two
independent experiments with identical excitation are used. The analysis is
asymptotic in the noise variance (i.e., as the standard deviation of the
innovations σ→ 0), for a finite data record of length N. We
highlight the relationship between the estimators accuracy and the loop shape
via asymptotic variance expressions given in terms of the sensitivity function.
The results are illustrated using a numerical simulation example.
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